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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural::Natural;
use crate::natural_polynomial::NaturalPolynomial;
use crate::natural_polynomial::arithmetic::mod_power_of_2_add::{add_assign_ref, add_assign_val};
use alloc::vec::Vec;
use malachite_base::num::arithmetic::traits::{ModPowerOf2IsReduced, ModPowerOf2Sum};
fn assert_reduced(p: &NaturalPolynomial, pow: u64) {
assert!(
p.mod_power_of_2_is_reduced(pow),
"every polynomial must be reduced mod 2^pow, but {p} has a coefficient >= 2^{pow}"
);
}
// Adds the polynomials' coefficients into one vector, reducing as it goes, and trims once at the
// end, since leading coefficients can cancel. Summands of different degrees are fine, and the sum
// of no polynomials is zero.
fn mod_power_of_2_sum_owned<I: Iterator<Item = NaturalPolynomial>>(
xs: I,
pow: u64,
) -> NaturalPolynomial {
let mut sum: Vec<Natural> = Vec::new();
for p in xs {
assert_reduced(&p, pow);
add_assign_val(&mut sum, p.coefficients, pow);
}
let mut sum = NaturalPolynomial { coefficients: sum };
sum.trim();
sum
}
fn mod_power_of_2_sum_ref<'a, I: Iterator<Item = &'a NaturalPolynomial>>(
xs: I,
pow: u64,
) -> NaturalPolynomial {
let mut sum: Vec<Natural> = Vec::new();
for p in xs {
assert_reduced(p, pow);
add_assign_ref(&mut sum, &p.coefficients, pow);
}
let mut sum = NaturalPolynomial { coefficients: sum };
sum.trim();
sum
}
impl ModPowerOf2Sum for NaturalPolynomial {
/// Adds up all the [`NaturalPolynomial`]s in an iterator modulo $2^k$, taking the polynomials
/// by value. The coefficients must already be reduced.
///
/// The summands may have different degrees, and the sum of no polynomials is zero.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $2^k$ and $\sum_
/// {i=0}^{n-1} p_i \equiv q \mod 2^k$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(m) = O(m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of coefficients of all
/// the polynomials, and $m$ is the greatest number of coefficients of any of them.
///
/// # Panics
/// Panics if any coefficient is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Sum;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x^2+2*x+3", "7*x+5", "x^3+7*x^2+6*x"]
/// .map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_power_of_2_sum(ps.into_iter(), 3).to_string(),
/// "x^3+7*x"
/// );
/// ```
#[inline]
fn mod_power_of_2_sum<I: Iterator<Item = Self>>(xs: I, pow: u64) -> Self {
mod_power_of_2_sum_owned(xs, pow)
}
}
impl<'a> ModPowerOf2Sum<&'a Self> for NaturalPolynomial {
/// Adds up all the [`NaturalPolynomial`]s in an iterator modulo $2^k$, taking the polynomials
/// by reference. The coefficients must already be reduced.
///
/// The summands may have different degrees, and the sum of no polynomials is zero.
///
/// $f((p_i)_ {i=0}^{n-1}) = q$, where every coefficient of $q$ is less than $2^k$ and $\sum_
/// {i=0}^{n-1} p_i \equiv q \mod 2^k$, coefficient by coefficient.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(m) = O(m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the total number of coefficients of all
/// the polynomials, and $m$ is the greatest number of coefficients of any of them.
///
/// # Panics
/// Panics if any coefficient is greater than or equal to $2^k$.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Sum;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let ps = ["x^2+2*x+3", "7*x+5", "x^3+7*x^2+6*x"]
/// .map(|s| NaturalPolynomial::from_str(s).unwrap());
/// assert_eq!(
/// NaturalPolynomial::mod_power_of_2_sum(ps.iter(), 3).to_string(),
/// "x^3+7*x"
/// );
/// ```
#[inline]
fn mod_power_of_2_sum<I: Iterator<Item = &'a Self>>(xs: I, pow: u64) -> Self {
mod_power_of_2_sum_ref(xs, pow)
}
}